Local noncuppability in R/M

Abstract

Given any [c], [a], [d] xxxxxxxxR/M such that [d] ≤ [a] ≤ [c], [a] is locally noncuppable between [c] and [d] if [d] < [a] ≤ [c] and [a] ∨ [b] < [c] for any [b] xxxxxxxxR/M such that [d] ≤ [b] < [c]. It will be shown that given any nonzero [c] xxxxxxxxR/M, there are [a], [d] xxxxxxxxR/M such that [d] < [a] ≤ [c] and [a] is locally noncuppable between [c] and [d].